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SUMMARY:Ron Rosenthal (Technion\, Israel)
DTSTART:20201204T050000Z
DTEND:20201204T060000Z
DTSTAMP:20260423T004659Z
UID:APATG/10
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/APATG/10/">R
 andom Steiner complexes and simplical spanning trees</a>\nby Ron Rosenthal
  (Technion\, Israel) as part of Asia Pacific Seminar on Applied Topology a
 nd Geometry\n\n\nAbstract\nA spanning tree of $G$ is a subgraph of $G$ wit
 h the same vertex set as $G$ that is a tree. In 1981\, McKay proved an asy
 mptotic result regarding the number of spanning trees in random $k$-regula
 r graphs\, showing that the number of spanning trees $\\kappa_1(G_n)$ in a
  random $k$-regular graph on $n$ vertices satisfies $\\lim_{n\\to\\infty}\
 \Big( \\kappa_{1}(G_n) \\Big)^{1/n}=c_{1\,k}$ in probability\, where $c_{1
 \,k}= \\frac{(k-1)^{k-1}}{(k^2-2k)^{\\frac{k-2}{2}}}$. \n\nIn this talk we
  will discuss a high-dimensional of the matching model for simplicial comp
 lexes\, known as random Steiner complexes. In particular\, we will prove a
  high-dimensional counterpart of McKay's result and discuss the local limi
 t of such random complexes. \n\nBased on a joint work with Lior Tenenbaum.
 \n
LOCATION:https://researchseminars.org/talk/APATG/10/
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